Rotational distributions from photodissociations. IV. The bent triatomic molecule

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Abstract
The generalized Franck–Condon theory for the photodissociations of bent triatomic molecules is formulated, including bending and rotational degrees of freedom. The nonseparable multidimensional Franck–Condon amplitudes are reduced to a rapidly convergent series of products of one-dimensional integrals. The Franck–Condon factors provide the photofragment quantum state distributions when inelastic scattering on the unbound surface is negligible. When the scattering is important, they provide the nascent amplitudes which are the driving terms in the full scattering treatment. Calculations of the expected photofragment rotational distributions are given under dipole and scalar couplings which are, respectively, appropriate to direct photodissociation and predissociations. Semiquantitative closed form WKB approximations to the Franck–Condon amplitudes are derived to exhibit the essential physical features of these amplitudes. The results are readily interpreted in terms of the Heisenberg uncertainty principle, the orientational constraints imposed by the bond angle of the bent triatomic molecule, and the conservation of angular momentum. A simple classical approximation is also used and results are in qualitative agreement to the quantal calculations. Comparisons are also provided with recent rotational distributions observed in H2S photodissociation and illustrative calculations are presented for predissociation of HCN from the C̃ state and direct photodissociation of HOCl from its ground state.